Bumpmap from grayscale in 2.8
Whoops! Turns out the material was already using nodes, I was just looking in the wrong place. I'd been looking for the material nodes in the "Texture Node Editor" view, but where they were actually located was in the "Shader Editor" view. From there, I was able to follow the instructions from the first answer to this question: Bump Map applique in Blender 2.8?